"Natural right" refers to a conception of humans having innate right to freedom.

I don't think we have freedom in a meaningful way. On a deserted island you'll have to work to survive. Progressives are in favor of meaningful freedom where you can do whatever you want and others have to pay the price. Conservatives are more based in reality. I think that's why people tend to be progressive when young and shielded from reality by parents but become more conservative as adults having to deal with reality.

It's pretty much impossible to define property rights well from the natural right standpoint. There are several gray areas, like air, water, pollution, light, sound and IPR. You can say that "everybody can do whatever they want as long as they don't harm others", but how do you define "harm"? It's very subjective concept that means different things to different people.

Chase Rachels wrote a great book on this: https://radicalcapitalist.org/2017/07/06/featured-content/
It first defines what can be property: that which is scarce. Which can change, so for example on earth oxygen isn't scarce and therefore not property. But on the moon it would be scarce and can therefore be property. The second component is that a human took it from nature. After that humans can trade property. Property can revert back to nature if humans abandon it. That's where there's some grey area, what does abandon mean exactly? This question will be answered through negotiations. In the same way prices are (mostly) determined now. Would you want a central controller determining what prices are or are you fine with using negotiations? People benefit enormously from cooperating with each other, so I'm not worried there will be a few outsiders unwilling to negotiate reasonably. They will simply be dissasociated from by others, which doesn't work with government in place.
Applying that to intellectual property, copyright and patents. All of these laws protect against uses of information that don't limit or restrict the creator of this information. Therefore the information isn't scarce. Less revenue for the creator is not property yet, therefore claimed losses of revenue cannot be claimed as violations of property. And therefore all of these laws are invalid. In the case of pollution; it's fine if you pollute nature - land not owned by anyone - but if someone fences it off and manages it, it become owned by them and pollution will have to be compensated for. It's notable that the worst pollution happens in the biggest countries and there's a 2/3 correlation between economic freedom and environmental quality. I think the causal relationship here is that rich people can afford to care about and take care of their environment. But government or common ownership of land certainly hasn't helped the environment.

Then try to maximize the well-being as much as possible

The big problem here is of course for whom? Humans have a biological bias in favor of women. Do we give them anything they want because that produces a greater percieved well-being? I don't think this will work.